Conversions About them Why we shouldn’t need them How to use them

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Measurements In SI, International System of Units, there are seven base units. Modern form of the metric system Three countries in the world have not adapted this system: Liberia, Myanmar and the United States.

Significant Figures A common convention used in science to indicate precision is known as significant figures. Significant figures are those digits in a measurement that are known with certainty plus the first digit that is uncertain.

Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.

Rules to Significant Figures

How many sig figs in the following measurements? 458 g g g g x

Adding and Subtracting The last sig fig in a measurement is an estimate. Your answer when you add or subtract can not be better than your worst estimate. have to round it to the least place of the measurement in the problem

For example l First line up the decimal places Then do the adding Find the estimated numbers in the problem This answer must be rounded to the tenths place

Practice = = = 6.2

Multiplication and Division Rule is simpler Same number of sig figs in the answer as the least in the question 3.6 x has 2 s.f. 653 has 3 s.f. answer can only have 2 s.f. 2400

Multiplication and Division Same rules for division 4.5 / = x = / =

Time for some practice- bet you can’t wait!!

Scientific Notation Means to express a number in it’s relation to 10’s Example: 8 x 10 2 Rule: Pos exponent = number bigger than zero Neg exponent = number smaller than zero

…Scientific Notation 8 x 10 2 Steps: Place a decimal behind the 8 Pos or Neg? Move the decimal the number of the exponent in the correct direction, add the zeros 8 =8 0 0= =

Scientific Notation Without a calculator

Sci. Not. – Multiplying and Dividing With exponents: Multiply the bases, then add the exponents Divide the bases, then subtract the exponents All answers MUST be in scientific notation

(2x10 3 ) x (4 x 10 5 ) 2 x 4 = = 8 8 x 10 8 (4x10 3 ) / (2 x 10 5 ) 4/2 =2 3-5= -2 2 x 10 -2

What if the answer isn’t in Sci. Not? (4x10 3 ) x (4 x 10 5 ) 4 x 4 = = 8 16 x 10 8 You must turn it into Sci. Notation If you move the decimal to the right, subtract an exponent If you move the decimal to the left, add an exponent 1.6 x 10 9

Sci. Not- Subtracting and Adding A little more work: When adding decimals, the places must be lined up Therefore, you cannot add two numbers who have different exponents (2 x 10 2 ) + (5 x 10 3 ) = 7 x

You must change one exponent into the other (2 x 10 2 ) + (5 x 10 3 ) Normal exponent rules apply (If you move the decimal to the right, subtract an exponent; If you move the decimal to the left, add an exponent) Make sure your answer is in Sci. Not. when you are finished

Measuring The numbers are only half of a measurement It is 10 long 10 what. Numbers without units are meaningless. How many feet in a yard A mile A rod

The Metric System AKA: SI system- International System of Units Easier to use because it is a decimal system Every conversion is by some power of 10. A metric unit has two parts A prefix and a base unit. prefix tells you how many times to divide or multiply by 10.

The Metric System King Henry Died Drinking Chocolate Milk KHD base dcm

Base Units Length - meter - m Mass - grams - g Time - second - s Temperature - Kelvin or ºCelsius K or C Energy - Joules- J Volume - Liter - L Amount of substance - mole - mol

Prefixes Kilo k 1000 times Deka 100 times Hecto 10 deci d 1/10 centi c 1/100 milli m 1/1000 kilometer - about 0.6 miles centimeter - less than half an inch millimeter - the width of a paper clip wire

Other Prefixes Signify the powers of 10

Example A typical bacterium has a mass of about 2.0 fg. Express this measurement in terms of grams and kilograms. Given: mass = 2.0 fg Unknown: mass = ? g mass = ? kg

Accuracy and Precision Accuracy: How close a measurement is to the exact value Precision: The degree of exactness of the measurement

Dimensional Analysis This is a structured way of helping you to convert units, and solve problems. With this method, you can easily and automatically convert very complex units if you have the conversion formulas.

Using Conversion Factors Make a fraction of the conversion formula, to convert units. For a unit to cancel it must appear on the top and the bottom of your dimensional analysis problem. Stayed tuned for examples…